Fuzzy c-means clustering of incomplete data using dimension-wise fuzzy variances of clusters

Abstract

Clustering is an important technique for identifying groups of similar data objects within a data set. Since problems during the data collection and data preprocessing steps often lead to missing values in the data sets, there is a need for clustering methods that can deal with such imperfect data. Approaches proposed in the literature for adapting the fuzzy c-means algorithm to incomplete data work well on data sets with equally sized and shaped clusters. In this paper we present an approach for adapting the fuzzy c-means algorithm to incomplete data that uses the dimension-wise fuzzy variances of clusters for imputation of missing values. In experiments on incomplete real and synthetic data sets with differently sized and shaped clusters, we demonstrate the benefit over the basic approach in terms of the assignment of data objects to clusters and the cluster prototype computation.